U.S. digital cellular communications uses digitized voice and data signals for communication between a mobile telephone and a base station. When the mobile moves, it may encounter degraded communication channels due to noise and multipath distortion; both noise and distortion varying with time. The multipath distortion is due to a signal being received by the mobile at different times when it bounces off buildings and terrain. Multipath channels can cause intersymbol interference (ISI) that can be removed with an adaptive equalizer, a specific type of an adaptive filter.
A typical adaptive filter is illustrated in FIG. 1. The input signal (106) is processed by the adaptive filter (101), producing the adaptive filter output signal (102). The output of the filter is then substracted (105) from a reference signal (103), to produce an error signal (104). This error signal (104) is used by an adaptive algorithm with an update coefficient, .mu., in the adaptive filter to update the filter coefficients. The update coefficient is also referred to as a tracking coefficient or memory coefficient. It is assumed that the memory of the adaptive algorithm increases as the value of .mu. increases.
The update coefficient controls the memory of the adaptive algorithm and its determination is a trade-off between the rate that the filter can track the changing channel characteristics and the amount of noise averaging that will be accomplished by the adaptive algorithm. As the adaptive algorithm memory is shortened, the algorithm is better able to track time variations in the communication channel but will become more sensitive to noise on the communication channel. If the coefficient is chosen to filter out more noise, then the filter's channel tracking capability will be reduced.
The adaptive algorithm can be a Kalman, Recursive Least Square, or Least Mean Square (LMS) algorithm. The typical goal of the adaptive algorithm is to minimize the mean square value of the error signal (104). This value is typically designated mean square error (MSE).
FIGS. 2A, B, and C illustrate the three possible classes of adaptive filter operating environments. FIG. 2A is a time invariant system in a noisy environment. In this case, the total MSE, designated E.sub.T, comes only from the noise, E.sub.n, in FIG. 2A since the system is not time varying. The total MSE is proportional to .mu..
FIG. 2B is a time varying but stationary system in a noisy environment; a stationary system having higher order signal statistics that do not change over time. In this example, E.sub.T (203) consists of the sum of two independent components, the lag error (201) and the noise (202). The lag error (201) is due to the filter attempting to track the time varying system. The lag error (201), designated E-lag, is inversely proportional to .mu.. The noise component (202) is due to the noisy environment as illustrated in FIG. 2A. It can be seen in FIG. 2B that the total MSE can be minimized by choosing the value of .mu. corresponding to the intersection of the curves (204).
The last environment is a time varying, non-stationary system in a noisy environment. The total MSE in this case consists of the same components as in FIG. 2B. The difference between the two systems is that in this case, the curves are shifting or changing slope over time causing the minimum point on the curve to shift thus changing the optimal value of .mu. over time. This environment is illustrated by comparing FIGS. 2B and 2C. FIG. 2B represents the MSE characteristic at some time t.sub.1 while FIG. 2C represents the MSE characteristic at some later time t.sub.2.
A fixed update coefficient in the last environment would not provide adequate filter performance due to the changing environment. There is a resulting need for automatically adapting the update coefficient according to the vehicle speed and channel conditions thereby improving filter performance.